P03GimbaledGyro-2DOF(2).ppt

1、Lecture 3 - Gimbaled gyro - 2DOF,1,Spinning Mass Gyroscope (continuing),质量自旋式陀螺（续）,Lecture 3 - Gimbaled gyro - 2DOF,2,6.1 Impulse response: IO,Impulse (脉冲) torque：-function, magnitude infinitely large and duration infinitely short, with limited area of integration.,Then L-transform system equations:

2、,Solving for (s) and (s)，we have,Lecture 3 - Gimbaled gyro - 2DOF,3,6.1 Impulse response,Lecture 3 - Gimbaled gyro - 2DOF,4,6.1 Impulse response: trajectory,Mx1 makes rotor axis oscillate around two ring axes, with /2 phase gap.,Eliminating t from the equations yields the trajectory (轨迹) :,Lecture 3

3、 - Gimbaled gyro - 2DOF,5,6.1 Impulse response: trajectory,Nutation: , center, radius, frequency,Lecture 3 - Gimbaled gyro - 2DOF,6,6.1 Impulse response: example,Let Jx = Jy = Je = 1.38 gcms2， H = 5160 gcms， Mx1 = 36200 gcm 10-5 s,(note: 1g = the weight of the mass of 1 gram),Radius of nutation,Feat

4、ures of nutation：high frequency and small magnitude,Lecture 3 - Gimbaled gyro - 2DOF,7,6.2 Step response: IO,When the applied torque is constant, it can be expressed as,Suppose all initial conditions are zeros, then the outputs in frequency domain are:,Lecture 3 - Gimbaled gyro - 2DOF,8,6.2 Step res

5、ponse: time domain,Dynamic response - nutation,Steady state response:,precession effective torsion spring,Lecture 3 - Gimbaled gyro - 2DOF,9,6.2 Step response: trajectory,Squaring and adding two sides yields the trajectory equation:,Lecture 3 - Gimbaled gyro - 2DOF,10,6.2 Step response: trajectory,C

6、ycloid (旋轮线): nutation + precession.,Speed of center,Tangent velocity,Lecture 3 - Gimbaled gyro - 2DOF,11,6.2 Step response: example,Drift rate,Nutation radius,Nutation frequency,Sources and impact of constant disturbance torque,Lecture 3 - Gimbaled gyro - 2DOF,12,6.3 Sinusoidal response: IO,If the

7、direction of the applied torque keeps alternating, typically it can be expressed as sinusoidal (正弦) function:,With zero initial conditions，frequency domain output:,Lecture 3 - Gimbaled gyro - 2DOF,13,6.3 Sinusoidal response: time domain,Terms:,Nutation Forced oscillation Constant,Lecture 3 - Gimbale

8、d gyro - 2DOF,14,6.3 Sinusoidal response: time domain,Lecture 3 - Gimbaled gyro - 2DOF,15,6.3 Sinusoidal response: reduction,Lecture 3 - Gimbaled gyro - 2DOF,16,6.3 Sinusoidal response: trajectory,Mx1 forces rotor axis to oscillate around two ring axes.,Eliminating time t yields trajectory:,Lecture 3 - Gimbaled gyro - 2DOF,17,6.3 Sinusoidal response: trajectory,Ellipse (椭圆):,Major and minor axes,Comparing influence of